Facebook is growing as the most popular social networking site available on the web. We had previously covered most commonly encountered Facebook Login issues. Facebook allows you to link other IDs with your Facebook account, which means if you have logged in with the linked ID, you will be automatically logged into Facebook. You can link Google, Yahoo, mySpace or other Open IDs to Facebook account.
To Link other IDs, open Account settings page (Click Account on the top right corner and select Account Settings)
Under the Settings, you can see the option Linked Accounts, select the account you want to link and click on the Link New Account button.
This will open the popup asking you to approve, the linking.
Once you allow your account to be linked to your Facebook account, it shows up in the list of accounts linked.
So next time you open Facebook, if you have logged into your linked account, then you are automatically logged into Facebook as well.